Please feel free to comment and add your own thoughts.
Spy: Usually goes straight for seductive lines. Slips in some French lines here and there.
Medic: Uses his deep voice. He knows it works. He knows people melt over that voice. Now, if he could just remember that surgery is a bad time to flirt… (“My, your pancreas is lovely.”)
Scout: Doesn’t really know what he’s doing, usually goes for pickup lines. He’s gotten better since “Expiration Date” though.
Heavy: Surprisingly shy, usually drops some compliments.
Engie: Pretty laid-back, his flirting is a bit subtle. Usually he tries to find something to do with the person he’s interested in, and uses it as an opportunity to drop compliments.
Demo: Fairly playful and energetic when flirting, but usually starts off by buying the person a drink. Will usually buy the person some flowers if he’s serious about it.
Soldier: Home-made gifts, usually the parts are gained from battle. We all saw that ear-necklace he made Zhanna…just wait til she gets the teeth earrings.
Sniper: Buys them a drink, waits for response before approaching. If they refuse the drink, it means no, unless they say otherwise. Tries to stay professional. Actually fairly reserved until he starts to get comfortable with the person he is flirting with.
Pyro: Tries to hand you some of their favorite things, will try to take you to the park…you get bonus points if you also enjoy burning things.
BUT WAIT! THERE’S MORE:
Saxton Hale: Shows off working out, brags about his adventures, tries to bond over beating up wild animals.
Merasmus: Hello? He has magic! He’s going to make a flower appear out of his hand, or maybe some butterflies. Heck, he’ll probably use his magic to make himself appear younger (and hotter), while he’s at it. That being said, take his magic away, and he hasn’t got a clue what to do.
Grey Mann: “Here is how this is going to work: I am a powerful man with a vast amount of wealth and I own a large company, and soon shall inherit another three (don’t ask me how, dear, now pay attention) By accepting my proposal, you will get in on all of it…” You get the idea: Overly confident and tries to use his wealth and power to win the person over. It must have worked, he has a daughter.
Nicholas Crowder/Old Nick: “Have you been Naughty or Nice?” (does eyebrow thing)
Ms. Pauling: Tries to start conversation, but gets overly nervous and giggly. She only ever gets one day off, she has not had a lot of time to practice.
The Administrator: Very blunt. If she wants you, she will tell you, and offer you one hour to decide if you are interested.